Open AccessSemi‐analytical solution for viscous Stokes flow in two eccentrically nested spheres
Author(s) -
Tosi Nicola,
Martinec Zdeněk
Publication year - 2007
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2007.03482.x
Subject(s) - spheres , stokes flow , finite element method , rotational symmetry , viscosity , spherical harmonics , mathematics , prandtl number , spherical geometry , flow (mathematics) , mechanics , mathematical analysis , geometry , physics , thermodynamics , heat transfer , astronomy
SUMMARY Applying the infinite Prandtl number approximation, a semi‐analytical solution for computing 2‐D axisymmetric viscous Stokes flow in a model consisting of two eccentrically nested spheres of different viscosities is derived. Since numerical codes based on spectral or finite techniques for modelling mantle flow in a spherical geometry in the presence of lateral viscosity variation are becoming more and more popular, reliable examples for testing and validating such codes are extremely useful. The eccentrically nested sphere solution was used to test a numerical algorithm based on a mixed spherical‐harmonic finite‐element formulation of the Stokes problem, and good agreement was obtained.